Abstract
The distributed finite-time control problem through adaptive neural identifier for a group of nonlinear agents with strict-feedback structure is assessed here. The main considered and assessed technical problems in this proposed control strategy are that followers’ states are not fully available for control design, and at the same time, each follower is represented by uncertain nonlinear switched dynamics. Due to the structure of the proposed followers here, a switched linear state observer is constructed to estimate the unavailable states. To finite convergence time guarantee, the backstepping design and finite-time approach are adopted in the distributed control design in a simultaneous manner. The control architecture is chosen to guarantee graph stability through multiple Lyapunov functions. It is revealed that the followers’ outputs are forced to follow the leader output in the finite time, and all signals in the overall closed-loop network system are assured to be bounded. Two simulation examples are presented to further demonstrate the validity of this proposed method.
Similar content being viewed by others
References
Olfati-Saber, R., Murray, R.M.: Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control 49(9), 1520–1533 (2004)
Li, T., Zhao, R., Chen, F.L., Philip, C.L., Liu, C.: Finite-time formation control of under-actuated ships using nonlinear sliding mode control. IEEE Trans. Cybern. 83(4), 1–11 (2018)
Yoo, S.J., Park, B.S.: Connectivity-preserving approach for distributed adaptive synchronized tracking of networked uncertain nonholonomic mobile robots. IEEE Trans. Cybern. (2017) . https://doi.org/10.1109/TCYB.2017.2743690
Li, S., Sun, H., Yang, J., Yu, X.: Continuous finite-time output regulation for disturbed systems under mismatching condition. IEEE Trans. Autom. Control 60(1a), 277–282 (2015)
Jiang, B., Hu, Q., Friswell, M.I.: Fixed-time rendezvous control of spacecraft with a tumbling target under loss of actuator effectiveness. IEEE Trans. Aerosp. Electron. Syst. 52(4), 1576–1586 (2016)
Olfati-Saber, R.: Flocking for multi-agent dynamic systems: algorithms and theory. IEEE Trans. Autom. Control 51(3), 401–420 (2006)
Hong, Y., Hu, J., Gao, L.: Tracking control for multi-agent consensus with an active leader and variable topology. Automatica 42(7), 1177–1182 (2006)
Ren, W.: On consensus algorithms for double-integrator dynamics. IEEE Trans. Autom. Control 58(6), 1503–1509 (2008)
Qin, J., Gao, H., Zheng, W.X.: Consensus strategy for a class of multi-agents with discrete second-order dynamics. Int. J. Robust Nonlinear Control 22(4), 437–452 (2012)
Li, Z., Ren, W., Liu, X., Fu, M.: Distributed containment control of multi-agent systems with general linear dynamics in the presence of multiple leaders. Int. J. Robust Nonlinear Control 23(5), 534–547 (2013)
Ma, Q., Lewis, F.L., Xu, S.: Cooperative containment of discrete-time linear multi-agent systems. Int. J. Robust Nonlinear Control 25(7), 1007–1018 (2015)
Mei, J., Ren, W., Li, B., Ma, G.: Distributed containment control for multiple unknown second-order nonlinear systems with application to networked Lagrangian systems. IEEE Trans. Neural Netw. Learn. Syst. 26(9), 1885–1899 (2015)
Zhang, H., Lewis, F.L.: Adaptive cooperative tracking control of higher-order nonlinear systems with unknown dynamics. Automatica 48(7), 1432–1439 (2012)
Shen, Q., Shi, P.: Output consensus control of multiagent systems with unknown nonlinear dead zone. IEEE Trans. Syst. Man Cybern. Syst. 46(10), 1329–1337 (2016)
Ren, C.-E., Chen, L., Chen, C.P.: Adaptive fuzzy leader-following consensus control for stochastic multiagent systems with heterogeneous nonlinear dynamics. IEEE Trans. Fuzzy Syst. 25(1), 181–190 (2017)
Wang, W., Huang, J., Wen, C., Fan, H.: Distributed adaptive control for consensus tracking with application to formation control of nonholonomic mobile robots. Automatica 50(4), 1254–1263 (2014)
Huang, J., Dou, L., Fang, H., Chen, J., Yang, Q.: Distributed backstepping-based adaptive fuzzy control of multiple high-order nonlinear dynamics. Nonlinear Dyn. 81(1–2), 63–75 (2015)
Shahvali, M., Askari, J.: Cooperative adaptive neural partial tracking errors constrained control for nonlinear multi-agent systems. Int. J. Adapt. Control Signal Process. 30(7), 1019–1042 (2016)
Shahvali, M., Shojaei, K.: Distributed adaptive neural control of nonlinear multi-agent systems with unknown control directions. Nonlinear Dyn. 83(4), 2213–2228 (2016)
Shen, Q., Shi, P.: Distributed command filtered backstepping consensus tracking control of nonlinear multiple-agent systems in strict-feedback form. Automatica 53, 120–124 (2015)
Cui, G., Xu, S., Lewis, F.L., Zhang, B., Ma, Q.: Distributed consensus tracking for non-linear multi-agent systems with input saturation: a command filtered backstepping approach. IET Control Theory Appl. 10(5), 509–516 (2016)
Chen, C.P., Wen, G.-X., Liu, Y.-J., Liu, Z.: Observer-based adaptive backstepping consensus tracking control for high-order nonlinear semi-strict-feedback multiagent systems. IEEE Trans. Cybern. 46(7), 1591–1601 (2016)
Wang, G., Wang, C., Yan, Y., Li, L., Cai, X.: Distributed adaptive output feedback tracking control for a class of uncertain nonlinear multi-agent systems. Int. J. Syst. Sci. 48(3), 587–603 (2017)
Shahvali, M., Askari, J.: Distributed containment output-feedback control for a general class of stochastic nonlinear multi-agent systems. Neurocomputing 179, 202–210 (2016)
Shahvali, M., Shojaei, K.: Distributed control of networked uncertain Euler–Lagrange systems in the presence of stochastic disturbances: a prescribed performance approach. Nonlinear Dyn. 90(1), 697–715 (2017)
Lee, S.W., Yoo, S.J.: Adaptive-observer-based output-constrained tracking of a class of arbitrarily switched uncertain non-affine nonlinear systems. Nonlinear Anal. Hybrid Syst. 24, 69–82 (2017)
Li, Y., Tong, S., Li, T.: Adaptive fuzzy backstepping control design for a class of pure-feedback switched nonlinear systems. Nonlinear Anal. Hybrid Syst. 16, 72–80 (2015)
Long, L., Zhao, J.: Decentralized adaptive fuzzy output-feedback control of switched large-scale nonlinear systems. IEEE Trans. Fuzzy Syst. 23(5), 1844–1860 (2015)
Zheng, Y., Ma, J., Wang, L.: Consensus of hybrid multi-agent systems. IEEE Trans. Neural Netw. Learn. Syst. 29(4), 1359–1365 (2018)
Zhu, Y., Zheng, Y., Wang, L.: Containment control of switched multi-agent systems. Int. J. Control 88(12), 2570–2577 (2015)
Lin, X., Zheng, Y.: Finite-time consensus of switched multiagent systems. IEEE Trans. Syst. Man Cybern. Syst. 47(7), 1535–1545 (2017)
Lin, X., Zheng, Y., Wang, L.: Consensus of switched multi-agent systems with random networks. Int. J. Control 90(5), 1113–1122 (2017)
Zhu, Y., Zheng, Y., Guan, Y.: Consensus of switched multi-agent systems under quantised measurements. Int. J. Syst. Sci. 48(9), 1796–1804 (2017)
Yoo, Sung Jin: Distributed consensus tracking of a class of asynchronously switched nonlinear multi-agent systems. Automatica 87(7), 421–427 (2018)
Du, H., He, Y., Cheng, Y.: Finite-time synchronization of a class of second-order nonlinear multi-agent systems using output feedback control. IEEE Trans. Circuits Syst. I Regul. Pap. 61(6), 1778–1788 (2014)
Khoo, S., Xie, L., Man, Z.: Robust finite-time consensus tracking algorithm for multirobot systems. IEEE/ASME Trans. Mechatron. 14(2), 219–228 (2009)
Meng, D., Jia, Y., Du, J.: Finite-time consensus for multiagent systems with cooperative and antagonistic interactions. IEEE Trans. Neural Netw. Learn. Syst. 27(4), 762–770 (2016)
Han, T., Guan, Z.-H., Liao, R.-Q., Chen, J., Chi, M., He, D.-X.: Distributed finite-time formation tracking control of multi-agent systems via FTSMC approach. IET Control Theory Appl. 11(15), 2585–2590 (2017)
Zhou, Y., Yu, X., Sun, C., Yu, W.: Higher order finite-time consensus protocol for heterogeneous multi-agent systems. Int. J. Control 88(2), 285–294 (2015)
Fu, J., Wang, J.: Robust finite-time containment control for high-order multi-agent systems with matched uncertainties under directed communication graphs. Int. J. Control 89(6), 1137–1151 (2016)
Wang, Y., Song, Y.: Fraction dynamic-surface-based neuroadaptive finite-time containment control of multiagent systems in nonaffine pure-feedback form. IEEE Trans. Neural Netw. Learn. Syst. 28(3), 678–689 (2017)
Zhao, L., Yu, J., Lin, C., Ma, Y.: Adaptive neural consensus tracking for nonlinear multiagent systems using finite-time command filtered backstepping. IEEE Trans. Syst. Man Cybern. Syst. (2017). https://doi.org/10.1109/TSMC.2017.2743696
Levant, A.: Robust exact differentiation via sliding mode technique. Automatica 34(3), 379–384 (1998)
Han, S.I., Ha, H., Lee, J.M.: Fuzzy finite-time dynamic surface control for nonlinear large-scale systems. Int. J. Fuzzy Syst. 18(4), 570–584 (2016)
Yoo, S.J.: Adaptive tracking control for uncertain switched nonlinear systems in nonstrict-feedback form. J. Frankl. Inst. 353(6), 1409–1422 (2016)
Zhao, X., Zheng, X., Niu, B., Liu, L.: Adaptive tracking control for a class of uncertain switched nonlinear systems. Automatica 52, 185–191 (2015)
Long, L., Zhao, J.: A small-gain theorem for switched interconnected nonlinear systems and its applications. IEEE Trans. Autom. Control 59(4), 1082–1088 (2014)
Tong, S., Li, Y., Sui, S.: Adaptive fuzzy output feedback control for switched nonstrict-feedback nonlinear systems with input nonlinearities. IEEE Trans. Fuzzy Syst. 24(6), 1426–1440 (2016)
Sun, Y., Chen, B., Lin, C., Wang, H.: Finite-time adaptive control for a class of nonlinear systems with nonstrict feedback structure. IEEE Trans. Cybern. (2017). https://doi.org/10.1109/TCYB.2017.2749511
Yu, J., Zhao, L., Yu, H., Lin, C., Dong, W.: Fuzzy finite-time command filtered control of nonlinear systems with input saturation. IEEE Trans. Cybern. 48(14), 2378–2387 (2018)
Wang, F., Chen, B., Lin, C., Zhang, J., Meng, X.: Adaptive neural network finite-time output feedback control of quantized nonlinear systems. IEEE Trans. Cybern. 48(6), 1839–1848 (2018)
Chen, M., Ge, S.S.: Adaptive neural output feedback control of uncertain nonlinear systems with unknown hysteresis using disturbance observer. IEEE Trans. Ind. Electron. 62(12), 7706–7716 (2015)
Fossen, T.I.: Guidance and Control of Ocean Vehicles. Wiley, Hoboken (1994)
Acknowledgements
This work was supported by the Ferdowsi University of Mashhad, Mashhad, Iran (Grant No. 44507)
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Rights and permissions
About this article
Cite this article
Shahvali, M., Pariz, N. & Akbariyan, M. Distributed finite-time control for arbitrary switched nonlinear multi-agent systems: an observer-based approach. Nonlinear Dyn 94, 2127–2142 (2018). https://doi.org/10.1007/s11071-018-4479-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-018-4479-4